Function generator

ABSTRACT

The invention comprises a means for providing a non-linear function. A first independent variable signal may be applied to a multiple switch variable gain circuit. A second independent variable signal, after being weighted by pulse width techniques in a sequencing circuit, controls the switching function of the variable gain circuit. The resultant signal is averaged and the output signal represents the first independent variable signal as a function of the second independent variable signal.

O United States Patent 1151 3,689,754 Le-Febre 1 Sept. 5, 1972 [54]FUNCTION GENERATOR 3,435,196 3/ 1969 Schmid ..235/ 150.53 t 2 Da A.3,513,301 5/1970 Howe ..235/150.53 [72] M Le mmmx Am 3,529,138 9/1970Andre et al ..235/15053 [73] Assignee: Sperry Rand Corporation.3,557,347 1/1971 Robertson ..235/ 150.53

[22] Flled: 1970 Primary Examiner-Joseph F. Ruggiero [21] Appl. No.:95,550 Attorney-8. C. Yeaton [52] US. Cl ..235/197, 235/150.53 [57] ABSCT [51] Int. Cl. ..G06g 7/36 Tm invention Comprises a means forProviding a [58] Field of Search ..235/197, 150.53, 150.3, 183, linearfunction A first independent variable signal 235/152; 340/347 D-347 A;307/229; ay be applied to a multiple switch variable gain cir- 328/142cuit. A second independent variable signal, after being weighted bypulse width techniques in a sequencing [561' References Cited circuit,controls the switching function of the variable gain circuit. Theresultant signal is averaged and the UNITED STATES PATENTS output signalrepresents the first independent variable t 3,226,641 12/1965 Miller..235/197 UX g' jg jjf functw mdepende yam 3,345,505 10/1967 Schmid..235/197 3,506,810 4/1970 Katell ..235/ 150.53 11 Claims, 2 DrawingFigures 42,," 27 1 C52 1 1s I 1 INPUT OUTPUT 2% o m 1 3,

45 4 AVERAGINB J l B I "fin VOLTAGE TO PULSE WIDTH I CONVERTER 1 2 3 4 5G 7 E 91011121314151G"'N ENABLE 1 OF N uscousa Till BINARY COUNTERPATENTEDsEP 51912 lNPUT GAIN CIRCUIT VARIABLE SHEET 1 BF 2 46 I RF I IOUTPUT AVERAGING CIRCUIT VOLTAGE TO PULSE WIDTH CONVERTER 22 3 35 r c 12 3 4 s s 7 s 9 1o 11121314151s---N CONTROL 364 INPUT SIGNAL ENABLE 1 OFN DECODER I RAMP 1 GENERATOR RESET 1 1 I CLOCK BINARY l 1 PULSES couNTERI/Vl/E/VTEJF F|G.l.

DAV/0 A. LE FEB/T PATENTEDSEP 5 I912 3.689.754

SHEET 2 OF 2 L CONTROL T MAXI INPUT CONTROL 37 INPUT L I W38 0 I TIME ORI I I I E I BIT 2 4 6 8 1o 12 14 INTERVAL IQ --DECODER| PERI00-- l TIMEOR BIT I l I I l I A b I I I I I I l I 2 4 e a DECODER OUTPUT PNO U GNIQQ TIME OR BIT INTERVAL TIM E OR B IT INTERVAL I/V VENTOR DA W0 4 L5FEBRE FUNCTION GENERATOR BACKGROUND OF THE INVENTION 1. Field of theInvention The present invention pertains to function generatorsparticularly of the type suitable for the generation of non-linearfunctions comprised of connected linear segments.

2. Description of the Prior Art Prior art function generators are knownthat generate non-linear functions comprised of connected linearsegments. One such function generator type in wide spread usage utilizesdiodes to determine the break points of the linear segments andrespectively associated resistors for determining the slopes thereof.These generators have numerous disadvantages. The variability of diodecharacteristics with changes in temperature causes inaccuracies, thusrequiring expensive and inconvenient environmental temperature controlor additional temperature compensation circuits. Additionally, thevariability of characteristics among commercially available diodes ofthe same type requires the inclusion of break point and slope adjustmentpotentiometers or selected resistors. In the design of a prior artgenerator, the component parameters are first calculated in accordancewith the function to be generated and thereafter complex empiricaladjustments to the numerous break point and slope potentiometers arerequired to correct for the variability of the diode characteristicsproviding an excessively time consuming and hence costly procedure.

An additional problem arising in the use of diode function generators isthat as the input voltage increases, the diodes are sequentially turnedon to provide the required break points of the generated function. Oncea diode has been turned on, it nonnally remains on as the input voltagecontinues to increase. Thus, the errors and inaccuracies due to thevariability of the diode characteristics tend to accumulate additivelyas the input voltage to the circuit increases resulting in inordinatelylarge errors at the high range of operating input voltages. Thevariability due to temperature changes further aggravates the problem.Additionally, since the break point and slope characteristics associatedwith a particular diode of a function generator are dependent upon thecharacteristics of the previously turned diodes, the calculationsrequired in the design of such diode function generators becomescumbersome.

Diode function generators are not particularly suited to bipolar inputvoltages, hence limiting the applicability of such devices.Additionally, they inherently provide monotonic functions and in orderto obtain nonmonotonic functions, the outputs of two such generators aresubtractively combined resulting in an excessive amount of equipment.

Several of the disadvantages associated with diode function generatorscan be obviated by utilizing an operational amplifier in combinationwith each required diode, the diode being connected in the feedback loopof the amplifier. In this manner, the effects of the variability of thediode characteristics are minimized. This approach has the disadvantageof requiring a large number of expensive operational amplifiers. Sincethe operating principles of such function generators are similar to thediode function generators,

the operational amplifier diode function generators also suffer frommany of the disadvantages previously discussed.

It is often desirable to provide in synchronism a variety of functionsof the same input variable. With prior devices a substantially completegenerator is required for each function to be provided, and the designsare not particularly suited to equipment saving, time sharingtechniques.

SUMMARY OF THE INVENTION The present invention provides a functiongenerator that overcomes the disadvantages discussed above utilizing aminimum of equipment compared to the prior art devices. The generator ofthe present invention provides one or more gain functions of respectiveindependent variable input signals under control ,of another independentvariable input signal.-

The desirable features of the present invention are achieved by afunction generator comprising a sequencing circuit that provides asequence of signals, the number of which is proportional to the controlinput signal. Variable gain means responsive to the sequence of signalsselectively provides predetermined gains corresponding to the sequenceof signals. An averaging circuit coupled to the variable gain meansprovides an output signal representative of the average of theselectively provided gains thus generating the required functions of thecontrol input signal.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a block schematic diagram ofa preferred embodiment of the invention; and

FIG. 2 is a waveform diagram illustrating waveforms useful in explainingthe operation of the preferred embodiment of the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT The preferred embodiment of thefunction generator of the present invention is particularly suited tothe generation of a gain function of an input signal under control ofanother input signal. For example, it is' often desirable to vary thegain of a servo of an aircraft autopilot as a function of the flightregimes of the aircraft in order to effect proper control in accordancewith the aircraft dynamics. This is particularly desirable in modern jettransports. This gain scheduling may be achieved by the presentinvention by connecting an aircraft attitude or rate sensor as an inputto the function generator of the invention, the output thereof beingapplied as the input signal to the associated servo. The

control input to the function generator may be derived from the airspeedoutput of the air data system of the aircraft. Thus, the gain of theautopilot servo is controlled as a function of airspeed.

Referring to FIG. 1, a preferred embodiment of the invention isillustrated as a function generator. A basic overall scheme of operatingwill first be discussed and followed by a detailed analysis. Thefunction generator is comprised of a sequencing circuit 21 responsive toan independent variable control input signal applied to a lead 22. Thesequencing circuit 21 provides a sequence of signals on control leads 23from decoder 31, the

total number turned on per period in the sequence being proportional tothe control input signal. The function generator further includes avariable gain circuit 24 responsive to particular individual outputs ofthe decoder 31. The variable gain circuit 24 provides predeterminedgains at terminal 26 of an independent variable input signal applied toterminal 25. The predetermined gains correspond respectively to theoutputs of decoder 31. The predetermined gains provided at the terminal26 are applied to anaveraging circuit 27 which in turn provides theaverage per period. Thus, a gain function of the signal at theterminal25 is generated in accordance with the control input signal applied tothe lead 22.

In more detail, the sequencing circuit 21 comprises a conventionalbinary counter 30 adapted to count clock pulses of any convenientfrequency. The outputs of the counter 30 are applied to a conventionalone of N decoder 31 that sequentially energizes its output control leads23 as the count from the counter 30 increases in response to the appliedclock pulses. FIG. 2c illustrates the sequence of signals provided onthe leads 23 (where N=16). It is understood that the counter 30 and thedecoder 31 comprise digital counting circuits of a type familiar topractitioners in the art.

The sequencing circuit 21 further includes a voltage to pulse widthconverter 32. The control input signal on the lead 22 is applied to thevoltage to pulse width converter 32 which in turn provides enablingpulses on a lead 33. The enabling pulses on the lead 33 have pulsewidths linearly proportional to the amplitude of the control inputsignal on the lead 22. The enabling pulses on the lead 33 are applied toan enable input of the decoder 31. Only during application of a pulse tothe enable input will the decoder 31 provide energization to the leads23. r

The voltage to pulse width converter 32 comprises a conventional rampvoltage generator 34 and a conventional voltage comparator 35. The rampgenerator 34 provides a ramp voltage signal to one of the inputs of thecomparator 35. The control input signal on the lead 22 is applied to thesecond input of comparator 35. The ramp generator 34 is reset inresponse to a predetermined count of the counter 30, which may forconvenience be the most significant bit count. In this manner, theoutput of the ramp generator 34 is synchronized to the counting periodof the counter 30. The comparator 35 provides the enabling pulses on thelead 33 where each enabling pulse is initiated coincident with theinitiation of the ramp signal and is terminated by the comparator 35when the ramp voltage equals the signal on the lead 22.

Referring now to FIGS. 1 and 2, the ramp voltage from the generator 34,the enabling pulses on the lead 33 and the sequence of signals on theleads '23 are illustrated in FIGS. 2a, b, and 0, respectively. For agiven level 36 of control input signal, the ramp voltage 37 equals thelevel 36 at a time 38 of the counter/decoder period. The time 38corresponding to the level 36 occurs half way between the initiation ofthe count of 9 and the count of of the counter 30. The enabling pulsescorresponding to this condition are illustrated in FIG. 2b. It isappreciated that the width of the enabling pulses illustrated isproportional to the control input signal level 36 of FIG. 2a aspreviously explained. Thus,

for the illustrated level 36, the decoder outputs 1 through 9 aresequentially energized providing a sequence of signals on the leads 23as illustrated in FIG. 20. In the example illustrated, the decoderoutputs 1-8 are energized for complete bit intervals while the decoderoutput 9 is energized for one-half of a bit interval. It is thereforeappreciated that the number of sequence signals provided by the decoder31 is linearly proportional to the enabling pulse width which in turn islinearly proportional to the control input signal on the lead 22. In theexample illustrated in FIG. 2, the number of sequence signals is 8.5. Itis therefore further appreciated that the sequencing circuit 21 providesa linear time quantization of the amplitude of the control input signalapplied to the lead 22.

Referring again to FIG. 1, the variable gain circuit 24 will bedescribed in more detail. Again controlling resistor R1 is connectedbetween terminals 25 and 26. Switches 42, 43 and 44 are also connectedbetween terminals 25 and 26 and selectively couple gain controllingresistors R2, R3 and R4, respectively. The resistors R3 and R4 arecoupled between the terminals 25 and 26 in a series circuit withinverter 45 for providing inverse polarity gains. The switches 4244 arecontrolled by logic gates 46, 47 and 48, respectively. An output on lead2 of the decoder 31 controls the logic gate 48 and the latter actuatesthe switch 44. Outputs on leads 3, 4 and 5 of the decoder 31 controlslogic gate 47 and thelatter actuates the switch 43. In a similar manner,outputs on control leads 9 and 10 control logic gate 46 and the latteractuates the switch 42. It is understood that the switches 42-44 andgates 46-48 are schematically illustrated and would normally beinstrumented by electronic switching circuits.

The terminal 26 of the variable gain circuit 24 provides an input to theaveraging'circuit 27 as previously explained. The averaging circuit 27which may, for example, comprise a lag circuit, includes an invertingoperational amplifier 51 with a capacitor 52 and a feedback resistor R,connected in shunt therewith. The time constant of the averaging circuit27 is chosen to be sufficiently long so that the operational amplifier51 provides a signal representative of the average of the signalsapplied thereto over the period of the counter/decoder 30-31. The outputof the averaging circuit 27 appears on output lead 53 and thus providesgain functions of the control input signal on the lead 22 with respectto input signals applied to the terminal 25.

Networks of the type comprising the terminal 25, the resistors R1-R4,the terminal 26, the operational amplifier 51 and the feedback resistorR,, generally have a gain relationship of the form (Waive) where thenegative sign associated with R; is caused by the inversion provided bythe amplifier 51. Thus specifically in the circuits 24 and 27, with noneof the switches 42-44 actuated, the gain from the input 25 to the outputis R,/R disregarding the averaging effect of the capacitor 52.Similarly, with the switch 44 actuated, the gain is R,{R R;/R.,. Whenthe switch 43 is actuated, the gains is -R,/R RylR, and when the switch42 is actuated, the gain is R,/R -R,lR It is appreciated that the signappearing in the gain expres- Gain: Q1ppm):

input sions associated with the resistors R and R are provided by theinverter 45.

The gains provided by the circuits 24 and 27, disregarding the averagingeffect of the capacitor 52, are illustrated in FIG. 2d. The lowfrequency roll off of the averaging circuit 27 prevents the circuits 24and 27 from providing the rapidly changing gain as illustrated. Instead,the averaging circuit 27 provides the average of the gains on the lead53 over the period of the counter/decoder 30-31 as previously explained.

It is now appreciated from the foregoing that during each period of thecounter/decoder 30-31, the leads 23 are sequentially energized beginningat least 1 and ending with the energization of one of the decoderoutputs from a complete or fractional bit interval in accordance withthe width of the enable pulses on the lead 33. Thus, the number of theleads 23 energized, including the fractional bit energization, islinearly proportional to the amplitude of the control input signal onthe lead 22. Since the gain controlling resistors R2, R3 and R4 arerendered effective by the switches 42, 43 and 44, respectively, which inturn are controlled by the leads 23, the variable gain circuit 24provides the predetermined gains corresponding to the bit intervals ofthe decoder 31 as illustrated in FIG. 2d.

When the control input signal on the lead 22 is, for example, at thelevel 36 (FIG. 2a), the variable gain circuit 24 provides thepredetermined gains illustrated in solid line in FIG. 2d. During bitinterval 1 none of the switches 42-44 are actuated, and the gain is R /RDuring bit interval 2, the switch 44 is actuated and the instantaneousgain drops to -R,/R R,/R During bit intervals 3, 4 and 5 the switch 43is actuated and the instantaneous gain becomes R,/R R,/R During bitintervals 6, 7 and 8 none of the switches 42-44 are actuated and theinstantaneous gain again becomes .R /R During the first half of bitinterval 9, the

switch 42 is actuated resulting in an instantaneous gain of -R /R1R /R2.During the second half of bit interval 9 and during the bit intervals10-16, none of the switches 42-44 are actuated and the gain againbecomes R;/R These predetermined gains provided during a period of thedecoder 31 are averaged by the circuit 27 and the output appears on thelead 53 as indicated by the legend of FIG. 2d. Generally, the averagegain during a period of the decoder 31 is the sum of the gains providedduring each bit interval thereof divided by the number of bit intervalsin the period.

Should the control input signal be at maximum level, as indicated by thelegend in FIG. 2, the predetermined gains provided by the circuit 24will be as shown in dotted line in FIG. 2d. Thus, for different levelsof control input voltage on the lead 22, different predetermined gainswill be selected during the period of the counter/decoder 30, 31providing different average gains on the lead 53.

It should be appreciated that in the bit interval during which theenabling pulse terminates, the active switch associated with that bitinterval is on for a time linearly proportional to the control inputsignal on the lead 22. Thus during that bit interval, the gain providedby the variable gain circuit 24 varies as a linear function of thecontrol input signal.

Analytically, the networks of the type comprising the circuits 24 and 27have a gain relationship in accordance with the expression R. an

When switch 43 is actuated during the entire intervals of 3 through 5the average gain is N R, N and when switch 42 is actuated for the entireintervals of 9 through 10 the average gain is R, R, We

During the operation of the function generator, illustrated in FIG. 1,the gain of the output 53 with respect to the input 25 varies as afunction of the control input signal on the lead 22. This function isillustrated by curve of FIG. 2e, the gain point 61 thereof correspondingto the average gain provided at the lead 53 in response to a controlinput signal at the level 36 as previously discussed.

The manner in which the gain curve 60 is derived will now be explained.For any control input signal of magnitude sufficiently small so thatonly decoder output 1 energizes during the decoder periods, none of theswitches 42-44 are actuated. Hence, the average gain G provided is R;/R,and the linear segment 62, over which the gain does not change, of thecurve 60 is generated. For control input voltages in the range betweenlevels 63 and 64, the length of time that the switch 44 is actuated islinearly proportional to the control input. When the control input is atthe level 64, the average gain G provided is R;/R l/N R,/R Because ofthe linearity relationship discussed, the average gain decreases fromR,/R, to R,/R l/N R /R as the control input voltage increases from level63 to level 64, hence generating the linear segment 65 of the curve 60.In a similar manner, the break points 66 and 67 have average gain valuesof G R,/R l/N R,/R., 3/N R lR and G R,/R, 1/N R /R 3/N R,/R 3/N R,/R 2/NR;/R respectively, thus generating the remainder of the connected linearsegments of the gain function 60. Parameters found suitable for thegeneration of the function 60 are R,= K,R 100K, R =59 K,R =47Kand R 19K.

It is now appreciated that the design of the variable gain circuit 24 toprovide the gain schedule 60 is a relatively simple additive processcompared to the design and adjustment of the prior art functiongenerators. The gain function break points are calculated as describedabove, where the values of the resistors determine the magnitudes of theslopes of the linear segments. The polarities of the slopes aredetermined by whether or not the signal applied to the terminal 25 isinverted by the inverter 45. When no switch is associated with a givenbit interval, the average gain remains the same over the range ofcontrol input signals associated therewith, resulting in a segment ofzero slope. Generally, a segment is generated by selecting the endpoints thereof an d calculating the gain required in the bit intervalsassociated therewith to change the average gain over the entire decoderperiod from that at the beginning of the segment to that at the end ofthe segment. From the foregoing it will be appreciated that the breakpoints of a generated function are accurately determined because of theclocked precision of the sequencing circuit 21. This accuracy issubstantially temperature insensitive compared to the prior art functiongenerators previously discussed.

Although the function generator provides a single gain function 60, itis appreciated that the sequencing circuit 21 may synchronously controlthe generation of a plurality of functions of the control input signalapplied to the lead 22. By appropriate gating, a plurality of variablegain circuits with associated averaging circuits may synchronouslyprovide the plurality of functions. Alternatively, logic circuitsinterposed between the decoder 31 and the gates 46-48 may program thevariable gain circuit 24 to provide a plurality of functions inaccordance with digital inputs to the logic circuits.

Although the sequencing circuit 21 is explained in terms of a counterand a decoder, other sequencing means such as shift registers orstepping circuits may be utilized to the same effect. Furthermore, thefunction generator may be used to control an output voltage as afunction of an input voltage similar in result to prior art functiongenerators. This may be accomplished by connecting the input voltage'toboth the lead 22 and the terminal 25.

It will be appreciated that the averaging effect of circuit 27 tends toprevent saturation of the amplifier 51 from occuring under adverselyhigh transient signal conditions. Hence, a significantly large dynamicrange is provided without scaling the voltages into the circuit.Additionally, the present invention can readily generate functionscomprising large numbers of linear segments because of the inherentsimplicity of the invention relative to the prior devices and becausethe present invention does not suffer from a reduction in dynamic rangewith large numbers of segments as do the prior devices.

The present invention may conveniently be tested for circuit failures bymeasuring the gain of the last break point of the generated functionwhen the control input voltage exceeds that required to provide thisbreak point. Simultaneous failures of equal magnitude, positive andnegative gain contributions may not be detectable by this method.However, this type of failure may be precluded by the appropriateselection of unequal positive and negative gains. A very high assuranceof failure detection may be achieved by gain measurements at the maximumand minimum inflection points of the gain function curve.

It will now be understood with respect to the aircraft servo applicationof the present invention, as previously discussed, that the aircraftattitude or rate sensor signal is applied to the input 25, the output 53being applied as the input to the servo and the airspeed signal beingapplied to the control input 22.

While the invention has been described in its preferred embodiment, itis to be understood that the words which have been used are words ofdescription rather than limitation and that changes may be made withinthe purview of the appended claims without departing from the true scopeand spirit of the invention in its broader aspects.

I claim:

1. Apparatus for generating functions of an input signal comprisingsequencing means responsive to said input signal for sequentiallyproviding a plurality of pulse signals, the total of the pulse durationsthereof being proportional to said input signal,

variable gain means responsive to said plurality of pulse signals forselectively providing a plurality of predetermined gains correspondingthereto, respectively,

means included in said variable gain means for rendering saidpredetermined gains effective during the durations of the correspondingpulse signals, and

averaging means coupled to said variable gain means for providing anoutput signal representative of the average of said selectively providedgains thereby providing said functions of said input signal.

2. The apparatus of claim 1 in which said sequencing means comprises aplurality of control leads, and

means for sequentially energizing a number of said control leads, allbut the last thereof being ener gized for equal time durations, the lastthereof being energized for a time duration linearly proportional tosaid input signal, thereby generating said plurality of pulse signals.

3. Apparatus for generating functions of an input signal comprisingsequencing means responsive to said input signal for providing asequence of signals the number thereof being proportional to said inputsignal,

variable gain means responsive to said sequence of signals forselectively providing predetermined gains corresponding to said sequenceof signals, respectively, and

averaging means coupled to said variable gain means for providing anoutput signal representative of the average of said selectively providedgains thereby providing said functions of said input signal,

said sequencing means comprising pulse width converter means forproviding enabling pulses of widths proportional to said input signaland digital counting means adapted'to count clock pulses and having aplurality of control leads for sequential energization in response tosaid clock pulses, said digital counting means being responsive to saidenabling pulses for enabling energization of said control leads onlyduring the presence thereof thereby providing said sequence of signals.

4. The apparatus of claim 1 in which said variable gain means comprises,

a plurality of gain controlling elements, and

switching means responsive to said plurality of pulse signals,

said gain controlling elements and said switching means being soarranged with respect to each other to provide said predetermined gains.

5. The apparatus of claim 1 in which said variable gain means comprisesa first terminal,

a second terminal,

a plurality of resistor means, and

switching means responsive to said plurality of pulse signals forselectively coupling said resistor means between said first and secondterminals thereby providing said predetermined gains.

6. The apparatus of claim 5 in which said variable gain means furtherincludes inverting means coupled in series circuit with respect tocertain of said resistor means between said first and second terminalsfor providing inverse polarity predetermined gains.

7. The apparatus of claim 1 in which said averaging means comprises lagcircuit means.

8. Apparatus for generating functions of an input signal comprisingpulse width converter means for providing enabling pulses of widthsproportional to said input signal,

digital counting means adapted to count clock pulses and having aplurality of control leads for sequential energization in response tosaid clock pulses,

said digital counting means being responsive to said enabling pulses forenabling energization of said control leads only during the presencethereof,

a first terminal,

a second terminal,

a plurality of resistor means,

a plurality of switching means coupled to said plurality of controlleads for selectively coupling said resistor means between said firstand second terminals thereby selectively providing predetermined gainswith respect to signals applied to said first terminal, and

averaging means coupled to said second terminal for providing an outputsignal representative of the average of said selectively provided gainsthereby providing said functions of said input signal.

9. The apparatus of claim 8 in which said pulse width converter meanscomprises ramp generator means coupled to said digital counting meansfor providing a ramp signal synchronized to a predetermined countthereof, and

comparator means responsive to said ramp signal and said input signalfor providing said enabling pulses to said digital counting means inaccordance with said ramp signal equalling said input signal.

10. The apparatus of claim 1 in which said sequencing means comprisespulse width converter means for providing enabling pulses of widthsproportional to said input signal, and

digital counting means adapted to count clock pulses and having aplurality of control leads for sequential energization in response tosaid clock pulses,

said digital counting means being responsive to said enabling pulses forenabling energization of said control leads only during he presencethereof thereby providing said plurality of pulse signals.

11. Apparatus for generating a function of an input signal, a point ofsaid function being generated during a predetermined time period, thecombination comprismg sequencing means responsive to said input signaladapted for sequentially providing a predetermined number of equalduration pulse signals, the total of the pulse durations thereof beingequal to said predetermined time period,

means included in said sequencing means for sequentially enabling saidpulse signals until the total pulse durations thereof are proportionalto said input signal, the duration of the last enabled pulse signalbeing linearly proportional to said input signal,

variable gain means coupled to said sequencing means adapted forproviding a predetermined number of predetermined gains corresponding tosaid predetermined number of pulse signals, respectively,

means included in said variable gain means for rendering effective thosepredetermined gains corresponding to said enabled pulse signals duringthe durations thereof, and

averaging means coupled to said variable gain means for providing anoutput signal representative of the average over said predetermined timeperiod of said predetermined gains rendered effective during said timeperiod, thereby providing said pointof said function of said inputsignal.

1. Apparatus for generating functions of an input signal comprisingsequencing means responsive to said input signal for sequentiallyproviding a plurality of pulse signals, the total of the pulse durationsthereof being proportional to said input signal, variable gain meansresponsive to said plurality of pulse signals for selectively providinga plurality of predetermined gains corresponding thereto, respectively,means included in said variable gain means for rendering saidpredetermined gains effective during the durations of the correspondingpulse signals, and averaging means coupled to said variable gain meansfor providing an output signal representative of the average of saidselectively provided gains thereby providing said functions of saidinput signal.
 2. The apparatus of claim 1 in which said sequencing meanscomprises a plurality of control leads, and means for sequentiallyenergizing a number of said control leads, all but the last thereofbeing energized for equal time durations, the last thereof beingenergized for a time duration linearly proportional to said inputsignal, thereby generating said plurality of pulse signals.
 3. Apparatusfor generating functions of an input signal comprising sequencing meansresponsive to said input signal for providing a sequence of signals thenumber thereof being proportional to said input signal, variable gainmeans responsive to said sequence of signals for selectively providingpredetermined gains corresponding to said sequence of signals,respectively, and averaging means coupled to said variable gain meansfor providing an output signal representative of the average of saidselectively provided gains thereby providing said functions of saidinput signal, said sequencing means comprising pulse width convertermeans for providing enabling pulses of widths proportional to said inputsignal and digital counting means adapted to count clock pulses andhaving a plurality of control leads for sequential energization inresponse to said clock pulses, said digital counting means beingresponsive to said enabling pulses for enabling energization of saidcontrol leads only during the presence thereof thereby providing saidsequence of signals.
 4. The apparatus of claim 1 in which said variablegain means comprises, a plurality of gain controlling elements, Andswitching means responsive to said plurality of pulse signals, said gaincontrolling elements and said switching means being so arranged withrespect to each other to provide said predetermined gains.
 5. Theapparatus of claim 1 in which said variable gain means comprises a firstterminal, a second terminal, a plurality of resistor means, andswitching means responsive to said plurality of pulse signals forselectively coupling said resistor means between said first and secondterminals thereby providing said predetermined gains.
 6. The apparatusof claim 5 in which said variable gain means further includes invertingmeans coupled in series circuit with respect to certain of said resistormeans between said first and second terminals for providing inversepolarity predetermined gains.
 7. The apparatus of claim 1 in which saidaveraging means comprises lag circuit means.
 8. Apparatus for generatingfunctions of an input signal comprising pulse width converter means forproviding enabling pulses of widths proportional to said input signal,digital counting means adapted to count clock pulses and having aplurality of control leads for sequential energization in response tosaid clock pulses, said digital counting means being responsive to saidenabling pulses for enabling energization of said control leads onlyduring the presence thereof, a first terminal, a second terminal, aplurality of resistor means, a plurality of switching means coupled tosaid plurality of control leads for selectively coupling said resistormeans between said first and second terminals thereby selectivelyproviding predetermined gains with respect to signals applied to saidfirst terminal, and averaging means coupled to said second terminal forproviding an output signal representative of the average of saidselectively provided gains thereby providing said functions of saidinput signal.
 9. The apparatus of claim 8 in which said pulse widthconverter means comprises ramp generator means coupled to said digitalcounting means for providing a ramp signal synchronized to apredetermined count thereof, and comparator means responsive to saidramp signal and said input signal for providing said enabling pulses tosaid digital counting means in accordance with said ramp signalequalling said input signal.
 10. The apparatus of claim 1 in which saidsequencing means comprises pulse width converter means for providingenabling pulses of widths proportional to said input signal, and digitalcounting means adapted to count clock pulses and having a plurality ofcontrol leads for sequential energization in response to said clockpulses, said digital counting means being responsive to said enablingpulses for enabling energization of said control leads only during thepresence thereof thereby providing said plurality of pulse signals. 11.Apparatus for generating a function of an input signal, a point of saidfunction being generated during a predetermined time period, thecombination comprising sequencing means responsive to said input signaladapted for sequentially providing a predetermined number of equalduration pulse signals, the total of the pulse durations thereof beingequal to said predetermined time period, means included in saidsequencing means for sequentially enabling said pulse signals until thetotal pulse durations thereof are proportional to said input signal, theduration of the last enabled pulse signal being linearly proportional tosaid input signal, variable gain means coupled to said sequencing meansadapted for providing a predetermined number of predetermined gainscorresponding to said predetermined number of pulse signals,respectively, means included in said variable gain means for renderingeffective those predetermined gains corresponding to said enabled pulsesignals during the durations thereof, and averaging means coupled tosaid variAble gain means for providing an output signal representativeof the average over said predetermined time period of said predeterminedgains rendered effective during said time period, thereby providing saidpoint of said function of said input signal.